It takes a lot of sustained effort and perseverance to autodidact (the process of self-learning). Learning Mathematics all by yourself could be harder. A bit of help will surely save considerable amount of time and accelerate things. I would like to present here some bits which I have found useful in this amazing cognitive delight.
• First; and foremost never, ever give up amidst any difficulty. Pick on what you feel like doing (interests) and don’t stop come whatever may!
• Pick your own corner in an ambient and cool isolated place, and immerse yourself into this ecstatic and immaculate process of enlightenment. Entangle the neuronal circuitry of your brain and provoke yourself with thoughts and nothing else. (Thought provoking isn’t it?) The greatest decision is to devote ourselves to understand the most fundamental and rudimentary.
• Don’t try to grasp everything from one book. Each book has its audience and difficulty level. So, take the advantage of this mere fact and exploit it! Segregate each book as per this criterion and that suits at this very instance.
• Don’t read theory and proofs like a machine/robot! Yes, we humans sometime sound like one! Mathematics is beautiful and there is, subtle beauty almost in every branch of it (feeling of this is certainly in our perception). Try to allocate enough time (can always be spend more than scheduled or planned time as it is satisfaction that is permanent). And yet again our approaches in problem solving also satisfies us. For example – One would always be contended & prefer neat solutions based on amalgam of ingenuity in thinking and intuition.
• Devise your very own way of working stuff out! You will be more satisfied than anything else. You will also gain more insight on rather subtle and abstract ways to think. Try out different ways of getting to a certain place.
• We can’t falsify the truth but in mathematics there is this — series of logical sequence of arguments which lead from hypothesis to proof. A mathematician really likes to prove and deduce things (important results!) and outline his approach.
• The thoughts we receive as we learn are a result of our understanding, mindset, beliefs, etc. Nothing is silly if we do label our doubts silly, it is rather plausible that we have not devoted the permissible time and effort. While it does partially reflect the way we perceive and judge things at an instance.